Behavior of Wire, Resistors, Capacitors, Inductors at High Frequencies

Dimensions and UnitsTo understand the upper frequency limit, beyond which conventional circuit theory can no longer be applied to analyze an electric system, we should recall the representation of an electromagnetic wave.

Dimensions and UnitsPropagation constant/Phase constant represents the change in phase per meter along the path travelled by the wave at any instant and is equal to the wave number of the wave.

Intrinsic impedance: the ratio between electric and magnetic field components.

TEM Waves: field components are perpendicular to each other and both are perpendicular to the direction of propagation.

Dimensions and UnitsTE Waves: in this magnetic field component is perpendicular to the direction of propagation.TM Waves: in this electric field component is perpendicular to the direction of propagation.The phase velocity of the TEM wave can be found as

RF Behavior of Passive ComponentsFrom the knowledge of circuit theoryR is frequency independentC and L are frequency dependentCapacitive and inductive reactance

For the low frequency; R, C and L are created by wires, plates and coils respectivelyPrinted circuit board (PCB) layout has frequency dependent resistance and inductance

Cond.DC excitationAC excitationSkin effectFor high frequency condition(f500MHz)

ConductivityCopper =64.516106S/mAluminum =40.0106S/mGold =48.544106S/m

CondFrom this we conclude that resistance increases inversely proportional to the cross-sectional skin area

AWG SystemDiameter of the wire is determined by its AWG valueGeneral rule: the diameter of the wire is doubles every six wire gauges starting with 1mil for a AWG 50 wire

High Frequency Resistors

c

Electric equivalent circuit representation of the resistorElectric equivalent circuit representation for high frequency wire-wound resistance

High Frequency CapacitorsIn RF/Microwave circuits chip capacitors find widespread applicationsTuning of filters Matching networksBiasing active components

Displacement currentAt high frequency, dielectric becomes lossy, there is a conduction current flow

Current flow at DC is due to the conductance,

CondLoss tangent is defined by the angle between the capacitors impedance vector and the negative reactive axis

Cond

Electric equivalent circuit for a high frequency capacitor

Loss TangentLoss tangent can also be defined as the ratio of an equivalent series resistance to the capacitors reactance

High Frequency InductorsRF/Microwave biasing networksRFCs (Matching and Tuning)Distributed capacitance and series resistance in the inductor coil

Equivalent circuit of the high-frequency inductor

High Frequency InductorsQuality factor: determines the resistive loss in the passive circuit